WTP Standard Error or 95% Confidence Intervals

[Lohas]

Greetings everyone,
I have successfully calculated the WTP in Nlogit, but how could I calculate the WTP Standard Errors and 95% Confidence Intervals for each WTP?
Thanks in advance,
Best regards,
Lohas

[Michiel Bliemer]

I am assuming that you are computing the WTP as a ratio of two coefficients, i.e. that you are considering two continuous attributes (of which one is price or cost) that are not dummy coded, i.e. WTP = b1 / b2.

The variance (and hence standard error) of WTP can then be computed using the Delta method, which requires b1, b2, var(b1), var(b2), and cov(b1,b2). You can find more about the Delta method in the literature.

Michiel

[Lohas]

I am assuming that you are computing the WTP as a ratio of two coefficients, i.e. that you are considering two continuous attributes (of which one is price or cost) that are not dummy coded, i.e. WTP = b1 / b2.

The variance (and hence standard error) of WTP can then be computed using the Delta method, which requires b1, b2, var(b1), var(b2), and cov(b1,b2). You can find more about the Delta method in the literature.

Michiel

Many thanks Michiel,
Yes, I did computed the WTP as a ratio of two coefficients, one is "Price", the other is a dummy coded un-continuous attribute. The syntax is as below:

?RPL model halton 1000
Nlogit
;lhs=choice
;choices=beef1,beef2,none
;checkdata
;rpl
;fcn=chan1(N),chan3(N),chan4(N),brand2(N),brand3(N),trace1(N),trace2(N)
;pts=1000
;halton
;pds=8
;wtp=brand3/price,trace1/price,trace2/price
;model:
U(product1)=chan1*channel1+chan3*channel3+chan4*channel4+brand2*brand2+brand3*brand3+trace1*trace1+trace2*trace2+price*price /
U(product2)=chan1*channel1+chan3*channel3+chan4*channel4+brand2*brand2+brand3*brand3+trace1*trace1+trace2*trace2+price*price /
U(none)=none
$
MATRIX ;list;1/232*1'wtp_i$

So, I calculated the WTP with the Syntax "wtp=brand3/price,trace1/price,trace2/price", and list them all together with the syntax "MATRIX ;list;1/232*1'wtp_i$".

I have searched our training PPT, that the Delta method got two pages of syntax, the first page is "Formula (Nlogit)", the second one is "Wald". So, does that mean I need to put all the two pages of syntax of "Delta method formula" and "Delta method Wald" after the syntax I wrote above?
Many thanks!

[Michiel Bliemer]

I have never used Nlogit so I cannot advice you regarding Nlogit, I can only provide advice regarding Ngene. Nlogit questions can be asked on the Nlogit online forum.

You do not need software to compute standard errors for ratios of coefficients, as I said you can simply manually apply the Delta method. The equation is for example given in Bliemer and Rose (2013) in Equation (10).

If WTP is w = b1/b2

then

se(w) = 1/b2 * sqrt( var(b1) - 2*b1/b2*cov(b1,b2) + (b1/b2)^2*var(b2) )

So all you need from Nlogit is the VARB covariance matrix from which you extract var(b1), cov(b1,b2), and var(b2). Together with estimates for b1 and b2 and the above equation, you obtain the requested standard errors.

Bliemer and Rose (2013) Confidence intervals of willingness-to-pay for random coefficient logit models. Transportation Research Part B, Vol. 58, pp. 199-214.

Feel free to make a reference to the amazing article above

Michiel